Find the area of quadrilateral whose diagonal is of length $70 m$ and lengths of the perpendiculars drawn from the opposite vertices on the diagonal are of lengths $42 m$ and $50 m$ respectively.

Open in App

Solution

Area $= \frac{1}{2} \times$ One diagonal $\times$ Sum of the length of the perpendiculars drawn from it on the remaining two vertices.
$= \frac{1}{2} \times 70 \times (42 + 50)$
$= 35 \times 92 = 3220 ‬$ sq.m

Suggest Corrections

Similar questions

Find the area of a quadrilateral one of whose diagonals is $40 c m$ and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are $16 c m$ and $12 c m$ .

Q. The length of the diagonal of a quadrilateral is

40 c m

and the perpendicular drawn to it from the opposite vertices are

12 c m a n d 7.5 c m

. Find the area of the quadrilateral.

Q. Find the length of a diagonal of a quadrilateral whose area is

195 m^{2}

and the lengths of the perpendicular to the diagonal vertices are

8.5 m

and

11 m

respectively.

Q. Find the area of a quadrilateral

A B C D

whose diagonal

A C

25 c m

long and the lengths of perpendicular from opposite vertices

B

and

D

A C

are

B E = 3.6 c m

and

D F = 2.4 c m

Q. Mark (✓) against the correct answer:
The diagonal of a quadrilateral is 20 cm in length and the lengths of perpendiculars on it from the opposite vertices are 8.5 cm and 11.5 cm. The area of the quadrilateral is
(a) 400 cm²
(b) 200 cm²
(c) 300 cm²
(d) 240 cm²

Join BYJU'S Learning Program

Find the area of quadrilateral whose diagonal is of length 70 m and lengths of the perpendiculars drawn from the opposite vertices on the diagonal are of lengths 42 m and 50 m respectively.

Area=12×One diagonal×Sum of the length of the perpendiculars drawn from it on the remaining two vertices.=12×70×(42+50)=35×92=3220‬sq.m

Find the area of quadrilateral whose diagonal is of length $70 m$ and lengths of the perpendiculars drawn from the opposite vertices on the diagonal are of lengths $42 m$ and $50 m$ respectively.

Area $= \frac{1}{2} \times$ One diagonal $\times$ Sum of the length of the perpendiculars drawn from it on the remaining two vertices.
$= \frac{1}{2} \times 70 \times (42 + 50)$
$= 35 \times 92 = 3220 ‬$ sq.m